with \(\Vert \varphi \Vert _{\infty }=\sup _{x\in \Omega }(\sum _{i=1}^d|\varphi _i(x)|^2)^{1/2}\) , “div” denotes the divergence operator, and \(C_c^{1}(\Omega ;\mathbb {R}^d)\)  is the set of once
continuously differentiable \(\mathbb {R}^d\) -valued functions with compact support in \(\Omega \) , see, e.g., [1]}, [2]} for more details. Moreover, the admissible set \(K\)  is
\(K:=\lbrace q\in L^{\infty }\cap BV(\Omega ):0<a_0\le q(x)\le a_1, \mbox{~a.e.~in~}\Omega \rbrace ,\) 
